Guzman Estrada
11/06/2023 · High School
QUESTION 8 The following information relates to the graph of \( f(x)=x^{3}+a x^{2}+b x-3 \) : \( f(-1)=f(3)=f^{\prime}(-1)=f^{\prime}\left(1 \frac{2}{3}\right)=0 \quad f\left(\frac{1}{3}\right)=-4 \frac{20}{27} \quad f\left(1 \frac{2}{3}\right)=-9 \frac{13}{27} \) The graph of \( y=f^{\prime}(x) \) is concave up and has a turning point at \( x=\frac{1}{3} \). \( 8.1 \quad \) Draw a neat sketch graph of \( f \) showing the intercepts with the axes, the turning points and the point of inflection. \( 8.2 \quad \) Calculate the value of \( a \) and \( b \).
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The values of \( a \) and \( b \) are \( a = -\frac{11}{3} \) and \( b = \frac{1}{3} \).
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